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NEET 2002
Exam
NEET
Year
2002
Subject
Physics
Chapter
Nuclear Physics

NEET 2002 · Physics · Nuclear Physics

A sample of radioactive element contains 4 × 10^ 16 active nuclei....

A sample of radioactive element contains 4×10164 \times 10^{16} active nuclei. The half-life of the element is 10 decays, then number of decayed nuclei after 30 days is:

Options

  1. A0.5×10160.5 \times 10^{16}
  2. B2×10162 \times 10^{16}
  3. C3.5×10163.5 \times 10^{16}
  4. D1×10161 \times 10^{16}

Correct answer

C. 3.5×10163.5 \times 10^{16}

Step-by-step solution

Half life number is given by n=1T=3010=3n=\frac{1}{T}=\frac{30}{10}=3 Nuclear of active nuclei left after n\mathrm{n} half-life isN=N0(12)n=4×1016(2)3=0.5×1016∴ Decay nuclei =N0−N=4×1016−0.5×1016=3.5×1016\begin{aligned}& N=N_0\left(\frac{1}{2}\right)^n \\ = & \frac{4 \times 10^{16}}{(2)^3}=0.5 \times10^{16} \\ \therefore & \text{ Decay nuclei }=N_0-N \\ = & 4 \times10^{16}-0.5 \times10^{16} \\ = & 3.5 \times10^{16} \end{aligned}
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